New Frontiers in Fields and Strings

The following sections are included:

• Preface
• TASI 2015 Group Photo: Identification List
• Contents

These notes are from courses given at TASI and the Advanced Strings School in summer 2015. Starting from principles of quantum field theory and the assumption of a traceless stress tensor, we develop the basics of conformal field theory, including conformal Ward identities, radial quantization, reection positivity, the operator product expansion, and conformal blocks. We end with an introduction to numerical bootstrap methods, focusing on the 2d and 3d Ising models.

We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of the main properties of Mellin amplitudes for CFT correlation functions and their uses in the context of AdS/CFT.

In these lectures we give an overview of the duality between gravitational theories of massless higher spin fields in AdS and large N vector models. We first review the original higher spin/vector model duality conjectured by Klebanov and Polyakov, and then discuss its generalizations involving vector models coupled to Chern-Simons gauge fields. We proceed to review some aspects of the theory of massless higher spins, starting with the Fronsdal equations for free fields and moving on to the fully non-linear Vasiliev equations in four dimensions. We end by reviewing some recent tests of the higher spin/vector model duality at the level of correlation functions and one-loop partition functions.

These notes attempt to provide some context for the study of stronglycorrelated quantum many body systems using quantum field theory.

In these notes, we review connections between quantum gravity and quantum information theory in the AdS/CFT correspondence. We describe connections between entanglement structure of the CFT state and geometrical structure of the dual spacetime. We describe constraints on entanglement and related quantities and show how these constrain gravitational dynamics in the dual theory.

The black hole information problem has been a challenge since Hawking’s original 1975 paper. It led to the discovery of AdS/CFT, which gave a partial resolution of the paradox. However, recent developments, in particular the firewall puzzle, show that there is much that we do not understand. I review the black hole, Hawking radiation, and the Page curve, and the classic form of the paradox. I discuss AdS/CFT as a partial resolution. I then discuss black hole complementarity and its limitations, leading to many proposals for different kinds of ‘drama.’ I conclude with some recent ideas.

Presented at the 2014-15 Jerusalem Winter School and the 2015 TASI.

Rotation curve measurements from the 1970s provided the first strong indication that a significant fraction of matter in the Universe is non-baryonic. In the intervening years, a tremendous amount of progress has been made on both the theoretical and experimental fronts in the search for this missing matter, which we now know constitutes nearly 85% of the Universe's matter density. These series of lectures provide an introduction to the basics of dark matter physics. They are geared for the advanced undergraduate or graduate student interested in pursuing research in high-energy physics. The primary goal is to build an understanding of how observations constrain the assumptions that can be made about the astro- and particle physics properties of dark matter. The lectures begin by delineating the basic assumptions that can be inferred about dark matter from rotation curves. A detailed discussion of thermal dark matter follows, motivating Weakly Interacting Massive Particles, as well as lighter-mass alternatives. As an application of these concepts, the phenomenology of direct and indirect detection experiments is discussed in detail.

Planning to explore the beginning of the Universe? A lightweight guide du routard for you.

These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires ‘ultraviolet completion’ because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the amplitude and shape of primordial tensor and scalar perturbations, and some of their correlation functions. Most backgrounds of string theory have positive potential energy, with a rich but still highly constrained landscape of solutions. The theory contains novel mechanisms for inflation, some subject to significant observational tests, with highly UV-sensitive tensor mode measurements being a prime example along with certain shapes of primordial correlation functions. Although the detailed ultraviolet completion is not accessible experimentally, some of these mechanisms directly stimulate a more systematic analysis of the space of low energy theories and signatures relevant for analysis of data, which is sensitive to physics orders of magnitude above the energy scale of inflation as a result of long time evolution (dangerous irrelevance) and the substantial amount of data (allowing constraints on quantities with signal/noise Portions of these lectures appeared previously in Les Houches 2013, "Post-Planck Cosmology".

TASI 2015 Participants